Question

How Do You Divide Derivatives?

Answer 1

Definition of Chain rule :

The rule applied for finding the derivative of the composite function (e.g. $\cos 2x,\log 2x,$etc.) is basically known as the chain rule. It is also called the composite function rule. The chain rule is applicable only for composite functions. So before starting the formula of the chain rule, let us understand the meaning of composite function and how it can be differentiated.

Chain rule formula :

The formula of the chain rule for the function $y=f\left(x\right),$ where $f\left(x\right)$is a composite function such that $x=g\left(t\right),$is given as:

$\frac{\mathbf{d}\mathbf{y}}{\mathbf{d}\mathbf{x}}\mathbf{=}\frac{\mathbf{d}\mathbf{y}}{\mathbf{d}\mathbf{u}}\mathbf{\times }\frac{\mathbf{d}\mathbf{u}}{\mathbf{d}\mathbf{x}}$

This is the standard form of chain rule of differentiation formula.

Another formula of the chain rule is represented by:

$\mathit{y}\mathbf{\text{'}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{d}}{\mathbf{d}\mathbf{x}}\mathbf{}\mathbf{(}\mathbf{}\mathit{f}\mathbf{(}\mathit{g}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{}\mathbf{)}\mathbf{}\mathbf{=}\mathbf{}\mathit{f}\mathbf{\text{'}}\mathbf{(}\mathit{g}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{)}\mathbf{}\mathbf{\times }\mathbf{}\mathit{g}\mathbf{\text{'}}\mathbf{(}\mathit{x}\mathbf{)}$

Hence, in this way we can divide derivatives.